A person is standing 15 meters away from a tree. If the angle of elevation to th

A person is standing 15 meters away from a tree. If the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

A person is standing 15 meters away from a tree. If the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

Correct Answer: 15 meters

Step 1: Understand the problem. You have a person standing 15 meters away from a tree.
Step 2: Know that the angle of elevation to the top of the tree is 45 degrees.
Step 3: Remember that the tangent (tan) of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the tree).
Step 4: For an angle of 45 degrees, the value of tan(45 degrees) is 1.
Step 5: Use the formula: Height = distance * tan(angle). Here, distance is 15 meters and tan(45 degrees) is 1.
Step 6: Calculate the height: Height = 15 * 1 = 15 meters.
Step 7: Conclude that the height of the tree is 15 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tree to the distance from the tree and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line of sight to the top of the object.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tree is the opposite side, the distance from the tree is the adjacent side, and the angle of elevation is the angle between them.